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# Addition of fractions with solved examples

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The addition of fractions is done easily when the given fractions have the same denominator. For instance, $\frac{1}{7} + \frac{2}{7} = \frac{3}{7}$. This directly means that whenever you are to add fractions, you have to make sure the given fractions have the same denominator before you go ahead to add their top numbers or numerators. Follow the guide below to add all kinds of fractions.

## Addition of improper fractions

An improper fraction is a kind of fraction whose denominator is less than or the same as the numerator. An example is shown below

Now let’s look at examples of how to add improper fractions. To add improper fractions you need to make sure your fraction have a common denominator. This can be done by finding the LCM of the denominators as shown in the examples below.

Example1. Perform the following operations below

a. $\frac{5}{3} + \frac{8}{5}\\$

b. $\frac{9}{3} + \frac{7}{4}$

Solution

a. $\frac{5}{3} + \frac{8}{5}\\$

= $\frac{(5×5) + (8×3)}{15}$

since the LCM of 3 and 5 is 15

= $\frac{25 + 24}{15} = \frac{49}{15}$

= 3$\frac{4}{15}$

b. $\frac{9}{3} + \frac{7}{4}$

= $\frac{(9×4) + (7×3)}{12}$

since the LCM of 4 and 3 is 12

= $\frac{36 + 21}{12} = \frac{57}{12} = 4\frac{9}{12}$

## Addition of Mixed numbers

Mixed numbers are fractions that have a whole number part and a fraction part written together. Examples of mixed fractions are shown

Example2. Add 3$\frac{1}{2} + 2\frac{2}{3}$

## Solutions

there are two ways of adding mixed numbers. First, add the whole number part and then the fractional part altogether.

$(3+2)(\frac{1}{2} + \frac{2}{3})\\$

=$5(\frac{(1×3) + (2×2)}{6}$)

= $5\frac{3 + 4}{6}\\$

= $5\frac{7}{6}\\$

= $\frac{(5×6) + 7}{6}\\$

= $\frac{30+7}{6}\\$

= $\frac{37}{6}\\$

= $6\frac{1}{6}\\$

Alternatively; work by using the LCM method.

$3\frac{1}{2} + 2\frac{2}{3} = \frac{(3×2) + 1}{2} + \frac{(2×3) + 2}{3}\\$

= $\frac{6 + 1}{2} + \frac{6 + 2}{3}\\$

= $\frac{7}{2} + \frac{8}{3}$

= $\frac{(7×3) + (8×2)}{6}$

Since the LCM of 2 and 3 is 6

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= $\frac{21 + 16}{6} = \frac{37}{6}\\$

= 6$\frac{1}{6}$